IRR is another Numerical Investment Appraisal Technique commonly used along with NPV by most of the appraisers. This indicates the Cost of Capital (CoC) that brings the NPV to zero (NPV = 0).
Not rocket science.....IRR is also a CoC but the speciality here is that, this particular CoC will bring your NPV to zero (No gain No loss position - neutral position).
For me IRR is also an indication of safety of the investment as you will know, from actual CoC how much it can vary until you reach this neutral point.
Let's get things started but before moving forward, you need to know the basics of NPV analysis. If you perfectly know the concept proceed but if you don't. keep your laziness away and read the below.
Let's take an investment opportunity and discuss the IRR concept. Sometimes questions are the only way to find explanations :)
Example :
An investment of $100 million on a machine that has a life of four (4) years to be evaluated. If the actual CoC is 10%, using the below data find the NPV and IRR.
Answer:
NPV Calulation
We have discussed the steps to calculate the NPV. It is just a matter of finding the PVs of the future cash flows and sum it.
At 10% actual CoC, the investment has a NPV of $24.38 million which is greater than zero (0). Hence, the potential investment opportunity is a feasible option.
IRR Calculation
This is where the game starts........
Let us check the NPV for different CoC. How to do this?? Don't think much but take random CoCs and calculate the NPV.
For better understanding I will do this for CoC 15%, 18% & 20%. Don't ever forget one thing, these are random CoCs but not the actual CoC. Acutal CoC is 10% which you already did a calculation for.
Did you figure out a relationship between CoC and NPV?? If not, check the 4th table again. When CoC increases, NPV tends to reduce.
Did the project change? No
Did the Cash flows change? No
Did the period change? No
Did the CoC change? Yes, this is the only factor that was changed and you see changes in NPV.
At 10% the NPV was at $24.38 million but at 20% the same set of cash flows has given a NPV of $(0.19) million.
Let me show this in a graph.
Our whole intention is to find the red dot point, where NPV is zero. The problem is, we will be using an interpolation method to find this point.
The equation to find the point will be given in most of the exams but this is not a difficult equation to remember. So do a lot of calculations are keep this in mind. It saves a lot of time.
Step by Step Approach
Pick a CoC which gives a positive NPV
Pick a CoC which gives a negative NPV
Use the formula and find the IRR
According to the calculation when CoC is 19.91%, the project would give you a NPV of zero. In other words, the project would reach the no gain, no loss point.
Key Points from the Analysis
At any CoC below IRR (CoC < 19.91%), the project would give a positive NPV indicating a viable project.
If the CoC changes and reach a point beyond IRR (CoC > 19.91%), the same project that gave you a positive NPV would give you a negative NPV indicating a loss from the project.
In above scenario, actual CoC (10%) is lower than IRR (19.91%) and there is a margin of 9.91% in CoC until it reaches a decision changing point. Isn't this like a margin of safety?
Calculation Tips
Always pick the CoCs which are closer to zero NPV. This is because interpolation technique is more like, finding a mid point. When you pick closer points you get a high accuracy.
If you do the NPV calculation at CoC 19.91%, you are supposed to get a NPV zero as that is the IRR but in reality you may get a NPV which is very closer to zero but not exactly zero. This is because you used a interpolation formula to reach a high accurate figure.
If you are to pick one project out of two potential projects, always give preference to NPV value and pick the project with higher NPV. You need to know how to evaluate investments with unequal life spans.
See, you won't get hold of these calculations unless you do a lot by yourself. Practice makes you perferct.
If you need me to discuss more questions, please leave a comment below. We will schedule a Q&A session.
Purindu B Jayatilake
MSc Eng (Reading), MBA, BSc (Hons) Eng, ACMA (UK), CGMA
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